Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x+2y &= 5 \\ 8x+4y &= 7\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -8x+7$ Divide both sides by $4$ to isolate $y$ $y = {-2x + \dfrac{7}{4}}$ Substitute this expression for $y$ in the first equation. $7x+2({-2x + \dfrac{7}{4}}) = 5$ $7x - 4x + \dfrac{7}{2} = 5$ Simplify by combining terms, then solve for $x$ $3x + \dfrac{7}{2} = 5$ $3x = \dfrac{3}{2}$ $x = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $x$ back into the top equation. $7( \dfrac{1}{2})+2y = 5$ $\dfrac{7}{2}+2y = 5$ $2y = \dfrac{3}{2}$ $y = \dfrac{3}{4}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = \dfrac{3}{4}$.